Question

rin is rolling a six-sided number cube repeatedly. Her goal is to roll a prime number 12 times.

How many times should Erin expect to have to roll the number cube to result in a prime number 12 times?

Enter your answer in the box to correctly complete the statement.

Erin should expect to roll the number cube approximately
times to result in a prime number 12 times.

Answer 1

To determine how many times Erin should expect to roll the number cube to get a prime number 12 times, we first need to identify how many prime numbers are on a six-sided die.

The prime numbers on a six-sided die (which has the numbers 1 through 6) are:
- 2
- 3
- 5

There are three prime numbers (2, 3, and 5) out of a total of six faces. This means the probability \( p \) of rolling a prime number is:

\[
p = \frac{3}{6} = \frac{1}{2}
\]

Now, we want Erin to roll a prime number 12 times. The expected number of rolls \( E \) needed to roll a prime number \( k \) times is given by the formula:

\[
E = \frac{k}{p}
\]

Here, \( k = 12 \) (the number of desired prime rolls) and \( p = \frac{1}{2} \).

Plugging in the values:

\[
E = \frac{12}{\frac{1}{2}} = 12 \times 2 = 24
\]

Thus, Erin should expect to roll the number cube approximately

\[
\boxed{24}
\]

times to result in a prime number 12 times.